Algebra Homework Help : Factoring the GCF in Algebraic Expressions

How to factor the GCF in an Algebraic Expression ?

Factoring the Greatest Common Factor (GCF) out of an algebraic expression involves three steps:
1. Find the GCF of all the terms in the algebraic expression.
2. Write the GCF outside the brackets.
3. Divide the terms in the original algebraic expression by the GCF and write them inside the brackets.

Example 1. 8x⁴ + 4x²−12x = 4x(2x³ + x − 3)
Here, the GCF is 4x.
Dividing each term in the original algebraic expression by 4x gives
8x⁴/(4x) = 2x³, 4x²/(4x) = x, and −12x/(4x) = −3.

Example 2. ab³ − 2a²b² = ab²(b − 2a)
Here, the GCF is ab².
Dividing each term in the original algebraic expression by ab² gives
ab³/(ab²) = b, and −2a²b²/(ab²) = −2a.

Note that it is important to check the answer by expansion.

Practice Exercise for Algebra Module on Factoring GCF in Algebraic Expressions